CANTON  Count on Cantor
One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.
1/1 1/2 1/3 1/4 1/5 ... 2/1 2/2 2/3 2/4 3/1 3/2 3/3 4/1 4/2 5/1
In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.
Input
The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.
Then, it contains a single number per line.
Output
You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.
Example
Input: 3 3 14 7 Output: TERM 3 IS 2/1 TERM 14 IS 2/4 TERM 7 IS 1/4
hide comments
epsilonalpha:
20160624 18:56:10
AC in first try, 0.06 seconds in Java. Just observe the pattern and the rest is very simple, no algorithm needed! 

rishabh_1997:
20160619 13:08:28
A very nice question... Just pick a paper & try to find the pattern


xinnix:
20160617 19:37:26
Easy but nice question. 

blueranger:
20160616 16:32:33
Easy ... AC in one go.... 0.00 Time !! 

top_gun007:
20160614 11:16:09
easy one 

gustavoaca1997:
20160610 07:44:16
Yeah! AC in 1 go, but I was thinking by many hours hehe. Thanks to the comments I searched and learned something that I did not know (I think that in my next trimester I'm going to study it): Triangular Numbers. Very useful! 

mkfeuhrer:
20160603 22:53:39
observe a while......get something diagonally related to sum ... AC in 1 go :) 

gkr007:
20160601 10:30:14
AC in 1 go :)!! 

bhushangawde:
20160516 08:10:43
easy AC in one go! :D My 20th !! 

satoruu:
20160423 00:21:21
Once you get the pattern, it will be easy. Think about math and geometry.

Added by:  ThanhVy Hua 
Date:  20050227 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL 6 VB.net 
Resource:  ACM South Eastern European Region 2004 